I need a help to solve this:
Find the points on the curve $x^2 + 4y^2 =4$ that are closest and furthest from the points on the curve $C: x^2 +y^2 +4x+2y=20$.
My try:
Let $f(x,y)=d^2(x,y)=(x-t)^2 + (y-s)^2$, with $(t,s) \in C$ and $g(x,y)=x^2 + 4y^2 =4$ restriction. I think something is missing...